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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6510 • Differentiable Manifolds

Fall 1996 • Question 6

Question

Math 6510 • Differentiable Manifolds Fall 1996 • Question 6

Take the 2-dimensional triangle \(T\) and identify all its sides as indicated below. What is the universal covering of the resulting topological space \(X\)?

Diagram description: the triangle \(T\) has all three sides identified. The left and right sides have arrows pointing toward the top vertex, and the bottom side has an arrow pointing from left to right.

Raw LaTeX

Take the 2-dimensional triangle \(T\) and identify all its sides as
indicated below. What is the universal covering of the resulting topological
space \(X\)?

\emph{Diagram description: the triangle \(T\) has all three sides identified. The left
and right sides have arrows pointing toward the top vertex, and the bottom side has
an arrow pointing from left to right.}

Topic Tags

Classification of Covering Spaces Covering Spaces Free Groups, Graph Coverings, and Presentations Point-Set Topology and Separation Theorems